Reconstruct a square wave with successive harmonics

Using four frequency components \( i = 1, 3, 5, 7 \), approximate the square wave.
The approximation shows \( \sum_{i} b_i\sin{\omega_i t} \), \( \omega_i = 2\pi i / \tau \).
Compare your empirical values with the prediction from the DFT below.

Questions

1. Compare your empirical values of \( b_i \) with the FT prediction \( b_i = 2 / ( \pi i ) \).
2. What happens to the slope of the rising edge as you add higher-harmonic components? (Relate this phenomenon to the idea that"bandwidth" translates to "speed.")
3. Does the DFT agree perfectly with the continuous FT prediction for small numbers of samples \( N \)? (Adjust the samples to the maximum to see what happens when the number of samples increases.)